Abstract
It is shown how an exact set of equations for the envelope functions may be derived, the method being illustrated using a one-dimensional model with uniform lattice constant. The exact equations allow one to identify the terms that are implicitly omitted in the standard envelope function approximation and give valuable insight into the reasons for the latter's success. It is also shown that the probability current can be expressed exactly in terms of the envelope functions; no averaging over a unit cell is needed. The generalisations of the above results to three dimensions are stated. The results reported here provide a method for the exact determination of electronic energy levels in microstructures no matter how small, or an approximate method in which the effects of omitted terms can be estimated.
Keywords
Envelope (radar)Exact solutions in general relativityLattice (music)Mathematical analysisMathematicsLattice constantFunction (biology)Constant (computer programming)Statistical physicsSemiconductorApplied mathematicsPhysicsQuantum mechanicsComputer scienceDiffraction
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Publication Info
- Year
- 1987
- Type
- article
- Volume
- 2
- Issue
- 7
- Pages
- 460-462
- Citations
- 33
- Access
- Closed
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Cite This
M G Burt
(1987).
An exact formulation of the envelope function method for the determination of electronic states in semiconductor microstructures.
Semiconductor Science and Technology
, 2
(7)
, 460-462.
https://doi.org/10.1088/0268-1242/2/7/012
Identifiers
- DOI
- 10.1088/0268-1242/2/7/012